Problem: What number could replace $k$ below? $\dfrac{1}{3} = \dfrac{2}{k}$
Solution: The fraction on the left represents 1 out of 3 slices of a rectangular pie. How many total slices would we need if we want the same amount of pie in 2 slices? We would need to cut the pie into 6 slices. $\dfrac{1}{3} = \dfrac{2}{6}$ and so the answer is $6$ Another way to get the answer is to multiply by $\dfrac{2}{2}$ $\dfrac{2}{2} = \dfrac{1}{1} = 1$ so really we are multiplying by 1. The final equation is: $\dfrac{1}{3} \times \dfrac{2}{2} = \dfrac{2}{6} $ so our answer is $6$.